Polar Star Quantitative Commodity Fund

Dr Mauritz van den Worm, PhD

28 November, 2018

Manual vs Automated Trading

How has the increase of Automated Trading Systems (ATS) influenced the futures market?

  • CME transaction data identitifies ATS with the 1028 tag
  • Data available from November 2012 to present
  • Consider data form 2012 to 2016
  • Use gradient plots to highlight the changes
  • Graphs are interactive

MAN vs ATS - Group

MAN vs ATS - Agriculture

MAN vs ATS - Energy

Trade Participation

Where are the opportunities?

  • Limited, Local, Spectrum
    • Less liquid parts of the curve
    • Changes to makro
    • Concentrated risk on asymmetric risk/reward trades


  • Quantitative
    • Harvest systematic risk premium from large universe of commodities
    • Rule based decision making process
    • Strategies inspired by descretional methodology

Literature

Grinold’s Fundamental Law of Active Portfolio Management

Law of active portfolio management

\[ \text{Performance} = \text{Skill} \times \sqrt{\text{Breadth}} \]

Suppose we are in a coin flipping casino

  • Flip coins in stead of futures
  • The coin is biased - \(P(\text{heads}) = 0.51\)

How does the betting work?

  • We have 1000 coins
  • The minimum wager is 1 coin
  • If you win you gain 1 coin
  • If you loose you loose 1 coin
  • There are 1000 tables with coin wagers
  • Games runs in parallel

What is the optimal way to allocate coins?

Two extremes

  • Bet 1000 coins on one coin flip
  • Bet 1 coin on 1000 coin flips

Expected Return

  • Single bet: \(0.51 \times 1000 + 0.49 \times (-1000) = 20\)

  • Multi bet: \(1000 \times [0.51 + 0.49 \times (-1)] = 20\)

The same expected return

Risk - Probability to lose it all:

  • Single bet: 49%

  • Multi bet: \(0.49 \times 0.49 \times \dots \times 0.49 = 0.49^{1000} \approx 0\)

Risk - Standard Deviation:

  • One coin per table

\[ \text{risk} := \text{std}\left\{1,-1,-1,1, \dots, 1 \right\} = 1 \]

  • One 1000 coin bet, 999 zero coin bets

\[ \begin{align} \text{risk} &:= \text{std}\left\{1000,0,0,0, \dots, 0 \right\} = 31.62 \\ \text{risk} &:= \text{std}\left\{-1000,0,0,0, \dots, 0 \right\} = 31.62 \end{align} \]

Coin Flip Casino - Reward/Risk

  • Just like Sharpe Ratio

  • Single bet: \(\text{SR}_{\text{single}} = \frac{20}{31.62} =0.63\)

  • Multi bet: \(\text{SR}_{\text{multiple}} = \frac{20}{1} =20\)

Coin flipping casino - Observation

  • \(20 = 0.63 \times \sqrt{1000}\)

  • \(\text{SR}_{\text{multiple}} = \text{SR}_{\text{single}} \times \sqrt{\text{Bets}}\)

  • \(\text{Performance} = \text{Skill} \times \sqrt{\text{Breadth}}\)

How does this apply to commodity futures?

  • We use insights gained from years of fundamental trading to inspire bespoke quantitative strategies that are applied to a large collection of commodity markets

  • We increase breadth or diversification by
    • how,
    • what and
    • when we trade

Literature

Technical considerations when trading futures systematically

  • Continuous Futures Price Series
    • We require long time series data
    • Futures expire too soon to gather sufficient data
    • How do you handle rolls?


  • Non-stationarity of Price Data
    • Time series data can only reliably be forecasted if stationary
    • Machine Learning algorithms are designed for stationary features
    • How do we create stationary data?

Continuous Futures Price Series

Continuous Futures Curves

Stationarity

Stationarity

How to obtain a stationary time series


  • Traditional
    • Price differences
    • Returns
    • Memory loss


  • Modern
    • Fractional differences
    • Memory present

Stationarity

Stationarity

Infrastructure

Core Strategies - Carry

Carry overview

  • Take advantage of curve shape
  • Contango is typically less steep in further dated contracts, i.e. it has a lower roll yield than near dated contracts
  • Extract roll yield with a short position in the near and a long position in the far dated contracts of the same commodity

Carry Example

Carry Example

Flavours of carry

  • ** Carry - inspired by discretionary methodology (BB)1**
    • 30 commodities and 2 tenors
    • Sizing determined using percentile methodology
    • Risk 0.5% of strategy NAV per trade
    • Monthly rebalance


  • ** Machine Learning Enhanced Carry (BB2)**
    • 30 commodities and 2 tenors
    • Fractionally differenced time-series
    • Meta labelling
    • Ensemble machine learning
    • Deterine probability of profitable trade and size trade accordingly

Backtest Assumptions

  • $10 Round trip of each contract
  • Slippage of 1 tick per contract


  • Entry cost of one spread \(= \text{\$}10 + 2 \text{ ticks} \times \text{multiplier}\)
  • Exit cost of one spread \(= \text{\$}10 + 2 \text{ ticks} \times \text{multiplier}\)

BB1 - Statistics

BB1 - Statistics

BB1 - Statistics

BB2 - Statistics

BB2 - Statistics

BB2 - Statistics

Systematic Carry - Statistics

Statistic BB1 BB2
Annualized Return 0.055 0.192
Annualized Sharpe (Rf=0%) 0.662 1.239
Annualized Std Dev 0.083 0.155
Average Negative Month Return -0.016 -0.028
Average Positive Month Return 0.019 0.044
Maximum Drawdown 0.267 0.395
Maximum Drawdown/Annualized Return 4.869 2.058
Number of Negative Months 103.000 95.000
Number of Positive Months 147.000 154.000

Carry literature

Literature on extracting carry from futures:

Literature on applying machine learing techniques in algorithmic trading:

Core Strategies - Trend

Trend overview

  • Trend following is about absolute performance of each commodity
  • Identify trends over selection of time frames
  • Slowly build position as trend increases
  • Slowly exit position as trend decreases
  • 35 Commodities and 2 tenors

Trend - Statistics

Trend - Statistics

Trend - Statistics

Trend - Statistics

Statistic TR1
Annualized Return 0.189
Annualized Std Dev 0.178
Annualized Sharpe (Rf=0%) 1.064
Maximum Drawdown 0.267
Maximum Drawdown/Annualized Return 1.410
Number of Positive Months 142.000
Number of Negative Months 107.000
Average Positive Month Return 0.057
Average Negative Month Return -0.035

Trend literature

Core Strategies - Relative Roll

Relative Roll overview

Strategy not yet live.

Relative Roll literature

Core Strategies - Sentiment

Sentiment overview

Strategy not yet live.

Sentiment literature

Quantitative Portfolio

Investment Thesis

  • Focus on the intersection of technolody, data and behavioral finance applied to the broad commodity space
  • Build strategies based on sound economic theory to help deliver long-term repeatable results. Inspired by
    • academic and
    • proprietary research.
  • Investment process built on the scientific method consisting of the systematic
    • observation,
    • measurement,
    • experiment,
    • hypothesis formulation,
    • testing and
    • modification of hypothesis

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Quantitative Portfolio - Statistics

Statistic 1998- 2008- 2015-
Annualized Return 0.200 0.191 0.061
Annualized Sharpe (Rf=0%) 1.706 1.654 0.658
Annualized Std Dev 0.117 0.115 0.093
Average Negative Month Return -0.021 -0.023 -0.023
Average Positive Month Return 0.041 0.042 0.029
Maximum Drawdown 0.187 0.137 0.128
Maximum Drawdown/Annualized Return 0.936 0.718 2.085
Number of Negative Months 100.000 54.000 23.000
Number of Positive Months 155.000 82.000 29.000

Polar Star Multi Strategy Portfolio

Polar Star Products and S&P500

Combine Discretionary and Systematic Portfolios

Polar Star Multi Strategy as enhancement to S&P500

Portfolio Comparison

Statistic S&P500 PS Multi Strategy PS Multi Strategy and S&P500
Annualized Return 0.129 0.154 0.145
Annualized Sharpe (Rf=0%) 1.139 1.524 1.931
Annualized Std Dev 0.113 0.101 0.075
Average Positive Month Return 0.028 0.029 0.022
Avereage Negative Month Return -0.024 -0.017 -0.014
Number of Negative Months 32.000 34.000 27.000
Number of Positive Months 64.000 62.000 69.000
Worst Drawdown 0.170 0.069 0.070

Summary

Combining a

  • discretionary and
  • systematic approach

to investing in commodities we create a product with

  • positive expected return which is
  • uncorrelated to equities

that gives superior risk adjusted returns.